Finite Group Databasebeta

← #25018531

Subgroups — #25018531

Order 11008.

1702 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582764C211yesmaximal, characteristic, complemented
2C2×#14582756C211yesmaximal, characteristic
3C2×#14582756C211yesmaximal, characteristic
4C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
5#19132855C212yesmaximal, complemented
6#19132843C212yesmaximal
7#19132833C212yesmaximal
8#19132825C211yesmaximal, characteristic, complemented
9#19132824C211yesmaximal, characteristic, complemented
10#19132822C212yesmaximal, complemented
11C2×C4×C4⋊C4×C43C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C22×C4⋊Dic43C2211yescharacteristic
15C22×(C2×D43)⋊C4C2212yes—
16C22×(C2×D43)⋊C4C2212yes—
17C22×(C2×D43)⋊C4C2211yescharacteristic
18C22×(C2×D43)⋊C4C2211yescharacteristic
19C22×C4×Dic43C2211yescharacteristic
20#14582764—24no—
21#14582756—24no—
22#14582756—24no—
23C4×(C2×D43)⋊C4C418yescomplemented
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2211yescharacteristic
34C22×C4⋊C4×C43C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C42×C43C2212yes—
37C22×C42×C43C2211yescharacteristic
38C4×C4⋊C4×C43—24no—
39C2×#95×C43C2212yes—
40C24×D43C2311yescharacteristic
41C23×Dic43C2312yes—
42C23×Dic43C2312yes—
43C23×Dic43C2311yescharacteristic
44C23×Dic43C2311yescharacteristic
45C23×Dic43C2311yescharacteristic
46C22×C4×D43—22no—
47C22×C4×D43—22no—
48C22×C4×D43—22no—
49C22×C4×D43—22no—
50C22×C4×D43—22no—
51C22×C4×D43—22no—
52C22×C4×D43C2×C414yes—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—22no—
55C2×C4⋊Dic43—22no—
56C2×C4⋊Dic43—22no—
57C2×C4⋊Dic43—22no—
58C2×C4⋊Dic43—22no—
59C2×(C2×D43)⋊C4—22no—
60C2×(C2×D43)⋊C4—22no—
61C2×(C2×D43)⋊C4—22no—
62C2×(C2×D43)⋊C4—22no—
63C2×(C2×D43)⋊C4—24no—
64C2×(C2×D43)⋊C4—24no—
65C2×(C2×D43)⋊C4—24no—
66C2×(C2×D43)⋊C4—24no—
67C2×(C2×D43)⋊C4—42no—
68C2×(C2×D43)⋊C4—42no—
69C2×(C2×D43)⋊C4C2×C414yes—
70C2×(C2×D43)⋊C4C2×C414yes—
71C2×C4×Dic43—22no—
72C2×C4×Dic43—22no—
73C2×C4×Dic43C2×C414yes—
74C43⋊#95—24no—
75C43⋊#95—24no—
76C43⋊#95—24no—
77C43⋊#95—24no—
78C43⋊#95—24no—
79C43⋊#95—42no—
80C43⋊#95—42no—
81C43⋊#95—42no—
82C43⋊#95C2×C414yes—
83C43⋊#95C2×C414yes—
84C23×C4×C43C2311yescharacteristic
85C23×C4×C43C2312yes—
86C23×C4×C43C2312yes—
87C23×C4×C43C2311yescharacteristic
88C23×C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43—22no—
90C2×C4⋊C4×C43—22no—
91C2×C4⋊C4×C43—22no—
92C2×C4⋊C4×C43—22no—
93C2×C4⋊C4×C43D414yes—
94C2×C4⋊C4×C43D414yes—
95C2×C42×C43—22no—
96C2×C42×C43—22no—
97C2×C42×C43—24no—
98C2×C42×C43—24no—
99C2×C42×C43—42no—
100C2×C42×C43C2×C414yes—
101#95×C43—24no—
102C24×C43C2411yescharacteristic
103C23×D43—21no—
104C23×D43—21no—
105C23×D43—21no—
106C23×D43—21no—
107C23×D43—21no—
108C23×D43—21no—
109C23×D43—21no—
110C23×D43—21no—
111C23×D43—21no—
112C23×D43—21no—
113C23×D43—21no—
114C23×D43—21no—
115C23×D43C22×C412yes—
116C23×D43#4112yes—
117C23×D43#4112yes—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—22no—
121C22×C4×C43—21no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—21no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—21no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—21no—
136C22×C4×C43—22no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—22no—
140C22×C4×C43C22×C412yes—
141C22×C4×C43C22×C412yes—
142C22×C4×C43C22×C412yes—
143C22×C4×C43C2×D414yes—
144C22×C4×C43C2×D412yes—
145C22×C4×C43C2×D414yes—
146C22×C4×C43C2×D412yes—
147C22×C4×C43#4112yes—
148C22×C4×C43#4112yes—
149C22×C4×C43#4112yes—
150C22×C4×C43#4112yes—
151C22×C4×C43#4112yes—
152C22×C4×C43#4112yes—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—22no—
171C22×Dic43—22no—
172C22×Dic43—22no—
173C22×Dic43—22no—
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—22no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—22no—
185C22×Dic43C22×C412yes—
186C22×Dic43C22×C412yes—
187C22×Dic43C22×C412yes—
188C2×C4×D43—28no—
189C2×C4×D43—28no—
190C2×C4×D43—28no—
191C2×C4×D43—44no—
192C2×C4×D43—44no—
193C2×C4×D43—44no—
194C2×C4×D43—44no—
195C4⋊C4×C43—28no—
196C4⋊C4×C43—28no—
197C42×C43—28no—
198C42×C43—48no—
199(C2×D43)⋊C4—28no—
200(C2×D43)⋊C4—28no—
201(C2×D43)⋊C4—48no—
202(C2×D43)⋊C4—48no—
203C4⋊Dic43—44no—
204C4⋊Dic43—44no—
205C4×Dic43—28no—
206C23×C43C23×C411yescharacteristic
207C23×C43C22×D411yescharacteristic
208C23×C43C22×D411yescharacteristic
209C23×C43C2×#4111yescharacteristic
210C23×C43C2×#4111yescharacteristic
211C23×C43C2×#4111yescharacteristic
212C23×C43C2×#4111yescharacteristic
213C23×C43C2×#4111yescharacteristic
214C23×C43C2×#4111yescharacteristic
215C23×C43C2×#4111yescharacteristic
216C23×C43C2×#4111yescharacteristic
217C23×C43H(5,𝔽2)11yescharacteristic
218C23×C43H(5,𝔽2)11yescharacteristic
219C23×C432−1+411yescharacteristic
220C23×C432−1+411yescharacteristic
221C22×D43—22no—
222C22×D43—22no—
223C22×D43—22no—
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—22no—
227C22×D43—22no—
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—22no—
231C22×D43—22no—
232C22×D43—22no—
233C22×D43—22no—
234C22×D43—22no—
235C22×D43—22no—
236C22×D43—22no—
237C22×D43—22no—
238C22×D43—22no—
239C22×D43—41no—
240C22×D43—41no—
241C22×D43—41no—
242C22×D43—41no—
243C22×D43—41no—
244C22×D43—41no—
245C22×D43—41no—
246C22×D43—41no—
247C22×D43—41no—
248C22×D43—41no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43#11714yes—
256C2×C4×C43—22no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—24no—
266C2×C4×C43—24no—
267C2×C4×C43—24no—
268C2×C4×C43—24no—
269C2×C4×C43—24no—
270C2×C4×C43—24no—
271C2×C4×C43—42no—
272C2×C4×C43—42no—
273C2×C4×C43—42no—
274C2×C4×C43—42no—
275C2×C4×C43—42no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—42no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—42no—
282C2×C4×C43—42no—
283C2×C4×C43#11714yes—
284C2×C4×C43#11714yes—
285C2×C4×C43C4×D414yes—
286C2×C4×C43C4×D414yes—
287C2×C4×C43#12114yes—
288C2×C4×C43#12314yes—
289C2×C4×C43#12414yes—
290C2×C4×C43#12614yes—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C4×D43—416no—
327#13875—431nomaximal, Sylow
328C22×C43C2×#11711yescharacteristic
329C22×C43C2×#11711yescharacteristic
330C22×C43C2×#11711yescharacteristic
331C22×C43C2×C4×D411yescharacteristic
332C22×C43C2×C4×D411yescharacteristic
333C22×C43#52011yescharacteristic
334C22×C43#52011yescharacteristic
335C22×C43C2×#12111yescharacteristic
336C22×C43C2×#12311yescharacteristic
337C22×C43C2×#12411yescharacteristic
338C22×C43C2×#12611yescharacteristic
339C22×C43#52911yescharacteristic
340C22×C43#52911yescharacteristic
341C22×C43#52911yescharacteristic
342C22×C43#52911yescharacteristic
343C22×C43#54011yescharacteristic
344C22×C43#54111yescharacteristic
345C22×C43#54211yescharacteristic
346C22×C43#54211yescharacteristic
347C22×C43#54611yescharacteristic
348C22×C43#54611yescharacteristic
349C22×C43#54611yescharacteristic
350C22×C43#54711yescharacteristic
351C22×C43#54811yescharacteristic
352C22×C43#54811yescharacteristic
353C22×C43#54811yescharacteristic
354C22×C43#55011yescharacteristic
355C22×C43#55211yescharacteristic
356C22×C43#55211yescharacteristic
357C22×C43#55211yescharacteristic
358C22×C43#55311yescharacteristic
359C22×C43#55311yescharacteristic
360C22×C43#55311yescharacteristic
361C22×C43#55511yescharacteristic
362C22×C43#55611yescharacteristic
363C2×D43—24no—
364C2×D43—24no—
365C2×D43—24no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C4×C43—24no—
379C4×C43—42no—
380C4×C43—44no—
381C4×C43—44no—
382C4×C43#38818yes—
383Dic43—42no—
384Dic43—42no—
385Dic43—42no—
386Dic43—82no—
387Dic43—82no—
388C2×#382—431no—
389C2×#380—431no—
390C2×#380—431no—
391C2×C4×C4⋊C4D4311yescharacteristic, complemented
392C2×C4×C22⋊C4—431no—
393#1443—432no—
394#1440—432no—
395#1437—432no—
396C4⋊#95—431no—
397C4⋊#95—431no—
398#1434—432no—
399C2×C43#228311yescharacteristic
400C2×C43C2×#38811yescharacteristic
401C2×C43#231411yescharacteristic
402C2×C43#235211yescharacteristic
403C2×C43#235211yescharacteristic
404C2×C43#235211yescharacteristic
405C2×C43#235411yescharacteristic
406C2×C43#242011yescharacteristic
407C2×C43#242111yescharacteristic
408C2×C43#242611yescharacteristic
409C2×C43#242711yescharacteristic
410C2×C43#248911yescharacteristic
411C2×C43#249011yescharacteristic
412C2×C43#249411yescharacteristic
413C2×C43#249511yescharacteristic
414D43—44no—
415C24×C4—431no—
416C22×C4⋊C4—431no—
417C22×C4⋊C4—431no—
418C22×C4⋊C4C2×D4311yescharacteristic
419C22×C4⋊C4C2×D4311yescharacteristic
420C22×C22⋊C4—431no—
421C22×C22⋊C4—431no—
422C22×C22⋊C4—432no—
423C22×C22⋊C4—432no—
424C22×C42—431no—
425C22×C42C2×D4312yes—
426C22×C42C2×D4311yescharacteristic
427#382—864no—
428#380—864no—
429#380—864no—
430C4×C4⋊C4—24no—
431C4×C22⋊C4—438no—
432C2×#95—431no—
433C2×#95—431no—
434C2×#95—432no—
435C2×#95—432no—
436C2×#95—432no—
437C2×#95—432no—
438C2×#95—432no—
439C2×#95—432no—
440C2×#95—432no—
441C2×#95—432no—
442C2×#95C2×D4312yes—
443C43#1387511yescharacteristic, complemented, Sylow
444C25—431no—
445C23×C4—431no—
446C23×C4—431no—
447C23×C4—431no—
448C23×C4—434no—
449C23×C4—432no—
450C23×C4—432no—
451C23×C4—862no—
452C23×C4—862no—
453C23×C4—862no—
454C23×C4—862no—
455C23×C4—862no—
456C23×C4—862no—
457C23×C4C22×D4311yescharacteristic
458C23×C4C22×D4312yes—
459C23×C4C22×D4312yes—
460C23×C4C22×D4311yescharacteristic
461C23×C4C22×D4311yescharacteristic
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—862no—
467C2×C4⋊C4—862no—
468C2×C4⋊C4—862no—
469C2×C4⋊C4—862no—
470C2×C4⋊C4—862no—
471C2×C4⋊C4—862no—
472C2×C4⋊C4D17214yes—
473C2×C4⋊C4C22⋊D4314yes—
474C2×C22⋊C4—434no—
475C2×C22⋊C4—434no—
476C2×C22⋊C4—862no—
477C2×C22⋊C4—862no—
478C2×C22⋊C4—862no—
479C2×C22⋊C4—862no—
480C2×C22⋊C4—864no—
481C2×C22⋊C4—864no—
482C2×C22⋊C4—864no—
483C2×C22⋊C4—864no—
484C2×C22⋊C4—1722no—
485C2×C22⋊C4—1722no—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—24no—
489C2×C42—24no—
490C2×C42—42no—
491C2×C42—434no—
492C2×C42—862no—
493C2×C42—862no—
494C2×C42C4×D4314yes—
495#95—24no—
496#95—434no—
497#95—434no—
498#95—864no—
499#95—864no—
500#95—864no—
501#95—864no—
502#95—864no—
503#95—1722no—
504#95—1722no—
505#95—1722no—
506C24—432no—
507C24—432no—
508C24—432no—
509C24—861no—
510C24—861no—
511C24—861no—
512C24—861no—
513C24—861no—
514C24—861no—
515C24—861no—
516C24—861no—
517C24—861no—
518C24—861no—
519C24—861no—
520C24—861no—
521C24C23×D4311yescharacteristic
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—432no—
545C22×C4—432no—
546C22×C4—432no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—868no—
566C22×C4—868no—
567C22×C4—868no—
568C22×C4—862no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—862no—
572C22×C4—862no—
573C22×C4—862no—
574C22×C4—862no—
575C22×C4—862no—
576C22×C4—862no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—1724no—
583C22×C4—1724no—
584C22×C4—1724no—
585C22×C4—1724no—
586C22×C4C2×C4×D4312yes—
587C22×C4C2×C4×D4312yes—
588C22×C4C2×C4×D4312yes—
589C22×C4C2×D17214yes—
590C22×C4C2×D17212yes—
591C22×C4#1062189812yes—
592C22×C4#1062189812yes—
593C22×C4#1062189812yes—
594C22×C4#1062189812yes—
595C22×C4#1062190012yes—
596C22×C4#1062190212yes—
597C22×C4C2×C22⋊D4314yes—
598C22×C4C2×C22⋊D4312yes—
599C4⋊C4—28no—
600C4⋊C4—28no—
601C4⋊C4—1724no—
602C4⋊C4—1724no—
603C22⋊C4—868no—
604C22⋊C4—868no—
605C22⋊C4—1728no—
606C22⋊C4—1728no—
607C42—28no—
608C42—48no—
609C42—868no—
610C23—434no—
611C23—862no—
612C23—862no—
613C23—862no—
614C23—862no—
615C23—862no—
616C23—862no—
617C23—862no—
618C23—862no—
619C23—862no—
620C23—862no—
621C23—862no—
622C23—862no—
623C23—862no—
624C23—862no—
625C23—862no—
626C23—862no—
627C23—862no—
628C23—862no—
629C23—1721no—
630C23—1721no—
631C23—1721no—
632C23—1721no—
633C23—1721no—
634C23—1721no—
635C23—1721no—
636C23—1721no—
637C23—1721no—
638C23—1721no—
639C23—1721no—
640C23—1721no—
641C23—1721no—
642C23—1721no—
643C23—1721no—
644C23—1721no—
645C23C22×C4×D4311yescharacteristic
646C23C22×C22⋊D4311yescharacteristic
647C23C22×D17211yescharacteristic
648C23#41×D4311yescharacteristic
649C23#41×D4311yescharacteristic
650C23C2×#1062190011yescharacteristic
651C23C2×#1062189811yescharacteristic
652C23C2×#1062189811yescharacteristic
653C23C2×#1062189811yescharacteristic
654C23C2×#1062189811yescharacteristic
655C23C2×#1062190211yescharacteristic
656C23#1306337011yescharacteristic
657C23#1306337111yescharacteristic
658C23#1306337211yescharacteristic
659C23#1306337311yescharacteristic
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—1722no—
697C2×C4—1722no—
698C2×C4—1722no—
699C2×C4—1722no—
700C2×C4—1722no—
701C2×C4—1722no—
702C2×C4—1722no—
703C2×C4—1722no—
704C2×C4—1722no—
705C2×C4—1722no—
706C2×C4—1722no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4—1722no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—17216no—
723C2×C4#1306328214yes—
724C2×C4#1306328314yes—
725C2×C4C4×C22⋊D4314yes—
726C2×C4C4×D17214yes—
727C2×C4#1306329914yes—
728C2×C4#1306330814yes—
729C2×C4#1306331314yes—
730C2×C4#1306331914yes—
731C22—864no—
732C22—864no—
733C22—864no—
734C22—1722no—
735C22—1722no—
736C22—1722no—
737C22—1722no—
738C22—1722no—
739C22—1722no—
740C22—1722no—
741C22—1722no—
742C22—1722no—
743C22—1722no—
744C22—1722no—
745C22—1722no—
746C22#117×D4311yescharacteristic
747C22C2×#1306328211yescharacteristic
748C22C2×#1306328311yescharacteristic
749C22C2×C4×C22⋊D4311yescharacteristic
750C22C2×C4×D17211yescharacteristic
751C22#1458337911yescharacteristic
752C22#1458338011yescharacteristic
753C22C2×#1306329911yescharacteristic
754C22C2×#1306330811yescharacteristic
755C22C2×#1306331311yescharacteristic
756C22C2×#1306331911yescharacteristic
757C22#1458343111yescharacteristic
758C22#1458343111yescharacteristic
759C22#1458343611yescharacteristic
760C22#1458343611yescharacteristic
761C22#1458350011yescharacteristic
762C22#1458350711yescharacteristic
763C22#1458351411yescharacteristic
764C22#1458352111yescharacteristic
765C22#1458353711yescharacteristic
766C22#1458354311yescharacteristic
767C22#1458354411yescharacteristic
768C22#1458355311yescharacteristic
769C22#1458355611yescharacteristic
770C22#1458356011yescharacteristic
771C22#1458356111yescharacteristic
772C22#1458357111yescharacteristic
773C22#1458358411yescharacteristic
774C22#1458358811yescharacteristic
775C22#1458359011yescharacteristic
776C22#1458359311yescharacteristic
777C22#1458359711yescharacteristic
778C22#1458359911yescharacteristic
779C22#1458361411yescharacteristic
780C22#1458362211yescharacteristic
781C4—24no—
782C4—44no—
783C4—44no—
784C4—42no—
785C4—3442no—
786C4—3442no—
787C4—1722no—
788C4—1722no—
789C4—1722no—
790C4#1458279018yes—
791C2—1724no—
792C2#1913699111yescharacteristic
793C2C2×#1458279011yescharacteristic
794C2#1913720011yescharacteristic
795C2#1913752011yescharacteristic
796C2#1913752511yescharacteristic
797C2#1913752711yescharacteristic
798C2#1913754211yescharacteristic
799C2#1913808111yescharacteristic
800C2#1913809211yescharacteristic
801C2#1913815511yescharacteristic
802C2#1913816611yescharacteristic
803C2#1913893011yescharacteristic
804C2#1913894111yescharacteristic
805C2#1913898911yescharacteristic
806C2#1913900011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C4×C4⋊C4×C43C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC2×C4×C4⋊C4D43
hypocenterC43#13875
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14582764C2semidirect
5. #19132855C2semidirect
8. #19132825C2semidirect
9. #19132824C2semidirect
10. #19132822C2semidirect
11. C2×C4×C4⋊C4×C43C2semidirect
23. C4×(C2×D43)⋊C4C4semidirect
391. C2×C4×C4⋊C4D43semidirect
443. C43#13875semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145827642
C2×#145827562
C2×C4×(C2×D43)⋊C42
#191328552
#191328432
#191328332
#191328252
#191328242
#191328222
C2×C4×C4⋊C4×C432
#1387543